A number of us went out together to a charity fete one day. Our party consisted of four different professional groups, namely – 25 writers, 20 doctors, 18 dentists and 12 bank employees. We spent altogether Rs. 1330.

Later it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists and that 6 dentists spent as much as 8 bank employees.

[Or, in other words: "A Writer spent (4/5) times the amount spent by a Doctor, a Doctor spent (3/4) times the amount spent by a Dentist and a Dentist spent (4/3) times the amount spent by a Bank Employee].

How much did each of the four professional groups spend ?

Let the respective amounts spent by all the writers, all the doctors, all the dentists and all the bank employees be a, b, c and d.

By the problem, the ratio between the amount spent by each writer, and each dentist is 4:5, and so a/b = 100/100 = 1

The ratio between the amount spent by each doctor, and that of each dentist is 4:5, and so b/c = 60/72 = 5/6

The ratio between the amount spent by each dentist, and each bank employee is 3:, and so c/d = 72/36 = 2

Consequently, a:b:c:d = 5:5:6:3, and thus:

(a,b,c,d) = (5x,5x,6x,3x) for some x.

By the given conditions, we must have:

5x+5x+6x+3x = 1330

Or, 19x = 1330, giving:

x = 70, so that:

(a,b,c,d) = (350, 350, 420, 210)

Consequently, the respective amounts spent by all the writers, all the doctors, all the dentists and all the bank emplorees are Rs. 350, Rs. 350, Rs.420 and Rs. 210.

*Edited on ***November 29, 2007, 12:19 pm**